The multifaceted destructions caused by COVID-19 have been compared to that of World War II. What makes the situation even more complicated is the ambiguity about the duration and ultimate spread of the pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an estimate of the future of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its derivatives, many investigators have tried to predict the outbreak of COVID-19. In this study, we simulated the epidemic in Isfahan province of Iran for the period from Feb 14th to April 11th and also forecasted the remaining course with three scenarios that differed in terms of the stringency level of social distancing. Despite the prediction of disease course in short-term intervals, the constructed SIR model was unable to forecast the actual spread and pattern of epidemic in the long term. Remarkably, most of the published SIR models developed to predict COVID-19 for other communities, suffered from the same inconformity. The SIR models are based on assumptions that seem not to be true in the case of the COVID-19 epidemic. Hence, more sophisticated modeling strategies and detailed knowledge of the biomedical and epidemiological aspects of the disease are needed to forecast the pandemic.

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Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.

Spalt-Like Transcription Factor 4 (SALL4) is a critical factor for self-renewal ability and pluripotency of stem cells. On the other hand, various reports show tight relation of SALL4 to cancer occurrence and metastasis. SALL4 exerts its effects not only by inducing gene expression but also repressing a large cluster of genes through interaction with various epigenetic modifiers. Due to high expression of SALL4 in cancer cells and its silence in almost all adult tissues, it is an ideal target for cancer therapy. However, targeting SALL4 meets various challenges. SALL4 is a transcription factor and designing appropriate drug to inhibit this intra-nucleus component is challenging. On the other hand, due to lack of our knowledge on structure of the protein and the suitable active sites, it becomes more difficult to reach the appropriate drugs against SALL4. In this review, we have focused on approaches applied yet to target this oncogene and discuss the potential of degrader systems as new therapeutics to target oncogenes.

Fibroblasts as key components of tumor microenvironment show different features in the interaction with cancer cells. Although, Normal fibroblasts demonstrate anti-tumor effects, cancer associated fibroblasts are principal participant in tumor growth and invasion. The ambiguity of fibroblasts function can be regarded as two heads of its behavioral spectrum and can be subjected for mathematical modeling to identify their switching behavior. In this research, an agent-based model of mutual interactions between fibroblast and cancer cell was created. The proposed model is based on nonlinear differential equations which describes biochemical reactions of the main factors involved in fibroblasts and cancer cells communication. Also, most of the model parameters are estimated using hybrid unscented Kalman filter. The interactions between two cell types are illustrated by the dynamic modeling of TGFβ and LIF pathways as well as their crosstalk. Using analytical and computational approaches, reciprocal effects of cancer cells and fibroblasts are constructed and the role of signaling molecules in tumor progression or prevention are determined. Finally, the model is validated using a set of experimental data. The proposed dynamic modeling might be useful for designing more efficient therapies in cancer metastasis treatment and prevention.